A vector calculation method for establishing inter-satellite links with different orbits

Abstract

The present invention provides a vector calculation method for establishing a link pointing between satellites in different orbits, including step A: obtaining the coordinates of the host satellite and the target satellite in the geocentric equatorial inertial coordinate system; step B: analyzing the geometric visibility of the target satellite; step C: obtaining the orbital normal vectors and +Z axis vectors of the host satellite and the target satellite; step D: calculating the pointing angle of the host satellite antenna through vector calculation and judging the direction; step E: calculating the pointing angle of the target satellite antenna through vector calculation and judging the direction. The present invention simplifies the link pointing angle calculation, which is convenient for non-satellite attitude professionals to quickly master.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to a vector calculation method for establishing a link between satellites on different orbits. Background Art

[0002] With the continuous development of remote sensing technology, the application of space facilities pays more and more attention to the coordinated detection and perception between satellites and constellations to exert and improve the system efficiency of space facilities. Promoting the establishment and integration of various satellites has become an inevitable trend in the development of aerospace technology.

[0003] Existing literature uses the method of converting the link vector to the local satellite orbit coordinate system and then calculating the pitch and azimuth angles for the calculation of intersatellite link pointing. The process not only requires multiple coordinate conversions, involving satellite attitude professional knowledge such as Euler angles and four elements, but also needs to be further converted into east / west angles and south / north angles before it can be used by antenna designers. The calculation process is complicated and difficult to understand. If the vector calculation method is used, you only need to know the coordinates of the local satellite and the target satellite in the same coordinate system to calculate the antenna pointing angle in real time. The calculation process only involves vector dot product and cross product operations, which is simple and easy to understand, and can be quickly mastered by non-satellite attitude professionals.

[0004] In the paper "Research and Performance Verification of Intersatellite Link Establishment and Pointing Algorithms" published in the Chinese Journal of Scientific Instrumentation in 2014, Teng Yunwanli, Wang Yueke, Chen Jianyun and others studied the intersatellite link antenna pointing algorithm. However, the algorithm adopted the method of Euler angle coordinate conversion to calculate the antenna pitch and azimuth pointing, which is a different technical path from the method of this patent using pure vector calculation to calculate the east / west and south / north pointing of the antenna.

[0005] In the paper "Intersatellite Link Antenna Pointing Modeling and Simulation Analysis" published in Computer Simulation in 2008, Lin Qi and Li Zhi proposed a method to calculate the elevation and azimuth pointing of satellite antennas based on the longitude and latitude coordinates of the sub-satellite point combined with spherical trigonometry. This method requires the sub-satellite point coordinates to be calculated in advance, and then the pointing calculation formula and its angle sign are selected according to the relative positions of the two satellites. The process is complicated and there is no unified calculation formula. This is a different technical path from the method of using pure vector operations to calculate the east / west and south / north pointing of the antenna in this patent. Summary of the invention

[0006] In view of the defects in the prior art, the object of the present invention is to provide a vector calculation method for establishing a link between satellites in different orbits.

[0007] A vector calculation method for establishing a link between satellites on different orbits provided by the present invention comprises the following steps:

[0008] Step A: Obtain the coordinates of the local and target satellites in the geocentric equatorial inertial coordinate system;

[0009] Step B: Analyze the geometric visibility of the target star;

[0010] Step C: Obtain the orbital normal vector and +Z axis vector of the local star and target star;

[0011] Step D: Calculate the pointing angle of the satellite antenna through vector calculation and determine the direction;

[0012] Step E: Calculate the target satellite antenna pointing angle through vector calculation and determine the direction.

[0013] Preferably, in step A, the local star is in a 0-inclination circular orbit, the target star is in an inclined circular orbit, and the semi-major axes of the two stars are both a.

[0014] Preferably, the position coordinates of this star are:

[0015]

[0016] The position coordinates of the target star are:

[0017]

[0018] Among them, u A and u B are the latitude arguments of the local star and the target star respectively, Ω is the right ascension of the ascending node of the target star, and i is the orbital inclination of the target star.

[0019] Preferably, in step B, the geometric visibility of the two satellites is obtained by judging whether the distance from the center of the earth to the geometric line connecting the two satellites is greater than 10 km of the earth radius.

[0020]

[0021] It is visible when d is greater than 10km of the earth's radius, otherwise it is invisible.

[0022] Preferably, in step C, the satellite body coordinate system coincides with the orbital coordinate system.

[0023] Preferably, when the own star and the target star are geometrically visible, obtain the orbital normal vector and +Z axis vector of the own star and the target star:

[0024] Normal vector of the local satellite orbital plane: N A =(0,0,1);

[0025] +Z axis vector in the local orbital coordinate system: Z A =(-cosu A , -sinu A , 0);

[0026] Normal vector of target star orbital plane:

[0027] +Z axis vector in the target star orbit coordinate system:

[0028] Preferably, in step D, the local satellite antenna direction is described using south / north angles and east / west angles.

[0029] Preferably, the link pointing vector is:

[0030] YOZ plane normal vector of the local satellite orbital coordinate system: N YOZ_A =N A ×Z A ;

[0031] Link pointing vector projection vector on YOZ plane: L prj_2_YOZ_A =N YOZ_A ×(L A ×N YOZ_A );

[0032] South / North Corner:

[0033] South / North direction: Sign α_A is the regular α A A positive value indicates that the angle is measured from +Z to the north in the YOZ plane. A negative value indicates that the angle is measured from +Z to the south.

[0034] Link pointing vector projection vector on XOZ plane: L prj_2_XOZ_A =N A ×(L A ×N A );

[0035] East / West Corner:

[0036] East / West corner direction: Sign β_A is the regular β A A positive value indicates that the angle is measured from +Z to the east in the XOZ plane. A negative value indicates that the angle is measured from +Z to the west.

[0037] Preferably, in step E, the target star antenna pointing is described using south / north angles and east / west angles.

[0038] Preferably, the link pointing vector: L B =-L A .

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. The present invention aims to solve the problem that the method of converting the link-building vector into the local satellite coordinate system and then calculating the antenna pointing in the existing different-orbit link-building pointing calculation process is complicated and difficult to master.

[0041] 2. The present invention simplifies the calculation of link pointing angles, making it easier for non-satellite attitude professionals to quickly master it. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0043] Figure 1 The figure is a flow chart of the steps of a method for calculating the vector of establishing a link between satellites in different orbits provided by an embodiment of the present invention;

[0044] Figure 2 FIG. 1 is a diagram showing the definition of two-star orbital parameters provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0046] like Figure 1 and Figure 2 As shown, a vector calculation method for establishing a link between satellites in different orbits provided by the present invention includes step A: obtaining the coordinates of the host satellite and the target satellite in the geocentric equatorial inertial coordinate system;

[0047] Step B: Analyze the geometric visibility of the target star;

[0048] Step C: Obtain the orbital normal vector and +Z axis vector of the local star and target star;

[0049] Step D: Calculate the pointing angle of the satellite antenna through vector calculation and determine the direction;

[0050] Step E: Calculate the target satellite antenna pointing angle through vector calculation and determine the direction;

[0051] In step A, the local satellite is in a 0-inclination circular orbit, the target satellite is in an inclined circular orbit, the semi-major axes of the two satellites are both a, and the position coordinates are:

[0052]

[0053]

[0054] Among them, uA and u B are the latitude arguments of the local star and the target star respectively, Ω is the right ascension of the ascending node of the target star, and i is the orbital inclination of the target star.

[0055] In step B: the geometric visibility of the two stars is obtained by judging whether the distance from the center of the earth to the geometric line connecting the two stars is greater than 10 km of the earth's radius.

[0056]

[0057] It is visible when d is greater than 10km of the earth's radius, otherwise it is invisible.

[0058] In step C: the satellite body coordinate system coincides with the orbital coordinate system, and when the local satellite and the target satellite are geometrically visible, the orbital normal vectors and +Z axis vectors of the local satellite and the target satellite are obtained:

[0059] Normal vector of the local satellite orbital plane: N A =(0,0,1);

[0060] +Z axis vector in the local orbital coordinate system: Z A =(-cosu A , -sinu A , 0);

[0061] Normal vector of target star orbital plane:

[0062] +Z axis vector in the target star orbit coordinate system:

[0063] Preferably, in step D, when the local satellite and the target satellite are geometrically visible, the antenna pointing angle is calculated:

[0064] Link pointing vector:

[0065] YOZ plane normal vector of the local satellite orbital coordinate system: N YOZ_A =N A ×Z A ;

[0066] Link pointing vector projection vector on YOZ plane: L prj_2_YOZ_A =N YOZ_A ×(L A ×N YOZ_A );

[0067] South / North Corner:

[0068] South / North direction: Sign α_A is the regular α AA positive value indicates that the angle is measured from +Z to the north in the YOZ plane. A negative value indicates that the angle is measured from +Z to the south.

[0069] Link pointing vector projection vector on XOZ plane: L prj_2_XOZ_A =N A ×(L A ×N A );

[0070] East / West Corner:

[0071] East / West corner direction: Sign β_A is the regular β A A positive value indicates that the angle is measured from +Z to the east in the XOZ plane. A negative value indicates that the angle is measured from +Z to the west.

[0072] In step E: when the local satellite and the target satellite are geometrically visible, the antenna pointing angle is calculated:

[0073] Link pointing vector: L B =-L A ;

[0074] The remaining calculations are the same as in step C.

[0075] In more detail, the present invention provides a vector calculation method for establishing link pointing between satellites in different orbits. The geometric visibility of the two satellites is analyzed according to the real-time position coordinates of the local satellite and the target satellite, and the antenna pointing angle is further obtained through vector operations. The calculation process only involves vector dot product and cross product operations, which is simple and easy to understand, and can be quickly mastered by non-satellite attitude professionals.

[0076] In order to make the purpose and features of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are further described below in conjunction with the accompanying drawings. The implementation steps are as follows: Figure 1 shown.

[0077] 1) Obtain the coordinates of the local and target satellites in the geocentric equatorial inertial coordinate system;

[0078] The semi-major axis a of both stars is 14371 km. A is -71°, u B is 48°, Ω is 10°, i is 37°, and the position coordinates of the two stars are:

[0079]

[0080]

[0081] 2) Analyze the geometric visibility of the target star;

[0082] d = 7317 km. It is larger than the radius of the earth (6371 km), so the two stars are visible.

[0083] 3) Calculate the pointing angle of the satellite antenna through vector calculation and determine the direction;

[0084] Link pointing vector:

[0085] Normal vector of the local satellite orbital plane: N A =(0,0,1);

[0086] +Z axis vector in the local orbital coordinate system: Z A =(-0.33, 0.95, 0);

[0087] YOZ plane normal vector of the local satellite orbital coordinate system: N YOZ_A =(-0.95,-0.33,0);

[0088] Link pointing vector projection vector on YOZ plane: L prj_2_YOZ_A =(-0.31,0.91,0.29);

[0089] South / North angle: α A =16.80°;

[0090] Link pointing vector projection vector on XOZ plane: L prj_2_XOZ_A =(0.14,0.99,0);

[0091] East / West angle: β A =26.97°;

[0092] 4) Calculate the target satellite antenna pointing angle through vector calculation and determine the direction;

[0093] Link pointing vector:

[0094] Normal vector of target star orbital plane: N B =(-0.10, -0.59, 0.80);

[0095] +Z axis vector in the target star orbit coordinate system: Z B =(0.53, 0.84, 0.13);

[0096] YOZ surface normal vector of the target star orbit coordinate system: N YOZ_B =(-0.75,0.44,0.23);

[0097] Link pointing vector projection vector on YOZ plane: L prj_2_YOZ_B =(-0.61,-1.08,0.05);

[0098] South / North angle: α B =21.86°;

[0099] Link pointing vector projection vector on XOZ plane: L prj_2_XOZ_A =(0.23,1.65,0);

[0100] East / West angle: β B =-23.50°.

[0101] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A vector calculation method for establishing a link between satellites in different orbits, characterized in that: The steps include: Step A: Obtain the coordinates of the local and target satellites in the geocentric equatorial inertial coordinate system; Step B: Analyze the geometric visibility of the target star; Step C: Obtain the orbital normal vector and +Z axis vector of the local star and target star; Step D: Calculate the pointing angle of the satellite antenna through vector calculation and determine the direction; Step E: Calculate the target satellite antenna pointing angle through vector calculation and determine the direction; In step A, the local star is in a 0-inclination circular orbit, the target star is in an inclined circular orbit, and the semi-major axes of the two stars are both a; The position coordinates of this star are: The position coordinates of the target star are: Among them, u A and u B are the latitude arguments of the local star and the target star, Ω is the right ascension of the ascending node of the target star, and i is the orbital inclination of the target star; In step C, the satellite body coordinate system coincides with the orbital coordinate system; When the own star and the target star are geometrically visible, obtain the orbital normal vector and +Z axis vector of the own star and the target star: Normal vector of the local satellite orbital plane: N A =(0,0,1); +Z axis vector in the local orbital coordinate system: Z A =(-cosu A , -sinu A , 0); Normal vector of target star orbital plane: +Z axis vector in the target star orbit coordinate system: In step D, the local satellite antenna direction is described by south / north angle and east / west angle; Link pointing vector: YOZ plane normal vector of the local satellite orbital coordinate system: N YOZ_A =N A ×Z A ; Link pointing vector projection vector on YOZ plane: L prj_2_YOZ_A =N YOZ_A ×(L A ×N YOZ_A ); South / North Corner: South / North direction: Sign α_A is the regular α A A positive value indicates that the angle is measured from +Z to the north in the YOZ plane; a negative value indicates that the angle is measured from +Z to the south. Link pointing vector projection vector on XOZ plane: L prj_2_XOZ_A =N A ×(L A ×N A ); East / West Corner: East / West corner direction: Sign β_A is the regular β A A positive value indicates that the angle is measured from +Z to the east in the XOZ plane; a negative value indicates that the angle is measured from +Z to the west.

2. The vector calculation method for establishing a link between satellites in different orbits according to claim 1 is characterized in that: In step B, the geometric visibility of the two stars is obtained by judging whether the distance from the center of the earth to the geometric line connecting the two stars is greater than 10 km of the earth radius. It is visible when d is greater than 10km of the earth's radius, otherwise it is invisible.

3. The vector calculation method for establishing a link between satellites in different orbits according to claim 1 is characterized in that: In step E, the target star antenna direction is described using south / north angles and east / west angles.

4. The vector calculation method for establishing a link between satellites in different orbits according to claim 3 is characterized in that: Link pointing vector: L B =-L A .

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